Topics+for+Semester+2+Exam

__**Topics for Semester 2 Exam - June 2012**__

EXPONENTS AND LOGARITHMS: laws of exponents, laws of logarithms, change of base, the exponential function f(x)=e x, the logarithmic function f(x)=ln x or log x, examples of compound interest, growth and decay

TRIGONOMETRY: definitions of sin, cos, tan, sec, csc, cot, arcsin, arccos, arctan, pythagorean identities, compound angle identities (including proofs), double angle identities (including proofs), trigonometric functions and their graphs, domains and ranges, solution of trigonometric equations

MATRICES: definition of a matrix, algebra of matrices, identity and zero matrices, determinants, inverse of a matrix, solutions of systems of equations using matrices, conditions for the existence of a unique solution, no solution and an infinity of solutions

VECTORS: definition of a vector, components of a vector, representations of vectors, sum and difference of vectors, zero vector, magnitude and direction, unit vectors, position vectors, scalar (dot) product of two vectors, parallel and perpendicular vectors, angle between two vectors, vector equation of a line (in 2-dimensions), angle between two lines

CALCULUS: derivatives of sin x, cos x, tan x, e x, a x , log x, ln x, arcsin x, arccos x, arctan x, chain rule, product rule, quotient rule, volumes of revolution, implicit differentiation, integration by substitution, integration by parts, differential equations by separation of variables